Surface Area and Volumes | CBSE Class 10 Revision and Important Questions

Surface Area and Volume Class 10 – Continuing our series for Class 10 Revision for CBSE board exams, we bring you a new chapter today i.e. Surface Area and Volume

Concepts to be covered in this article are:

Important formulae related to surface areas and volumes

Surface area and Volume of combination of solids

Conversion of solids from one shape to another

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Let’s take every topic of Surface Area and Volume one-by-one

Important formulae related to surface areas and volumes

This is a formula based chapter and you should be thorough with the formulae of total SA, lateral surface area and volume of basic solid figures, namely, cube, cuboid, cylinder, cone, frustum of a cone, sphere and hemi sphere.
Let us have a look at these formulae and then solve a ques based on them:

Lets solve a formula based question which has come in boards:
Q1. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Sol: Over here, note that whenever only SA is mentioned, we take total SA unless curved word is specified in the question.
Let the rad of hemisphere be 𝑟 units, then,
3𝜋𝑟^2=2/3𝜋𝑟^3
⇒𝑟=9/2 units
∴ Diameter =2𝑟=9 units

Surface area and Volume of combination of solids:

While calculating the SA and Volume of combination of solids, we need to modify the formulae for surface areas and volumes of basic solid figures to find the surface areas and volumes of a combination of these figures.

While calculating the surface area of a combination of solids, we need to exclude those surfaces that overlap each other on combining the solids

While calculating their volume, we either add or subtract the volumes of the two solids depending on the nature of the combination.

Lets solve a few questions that have been asked in boards previously based on this concept:
Q2. In figure, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 𝑚 and 3 𝑚 respectively and the slant height of conical part is 2.8 𝑚, find the cost of canvas needed to make the tent if the canvas is available at the rate of ₹ 500/sq. metre. (Use 𝜋=22/7)

Conversion of solids from one shape to another:

A lot of times questions are asked in which shape of solid changes: this can happen when a solid is melted and recast as another solid or a liquid is transferred from one container to another having a different shape. We need to keep in mind that in such
cases as the shape changes, the surface area will change. But the total volume will remain constant.

Lets solve a question based on this:
Q4. In a rain–water harvesting system, the rain–water from a roof of 22 𝑚×20 𝑚 drains into a cylindrical tank having diameter of base 2 𝑚 and height 3.5 𝑚. If the tank is full, find the rainfall in 𝑐𝑚. Write your views on water conservation.

Sol. Let the roof be filled up to a height ℎ. Then,

Vol of water collected on the roof = Vol of water collected in cylindrical tank
⇒22 ×20×ℎ=𝜋(1)^2×3.5
⇒ℎ=1/40𝑚=2.5 𝑐𝑚